That's how it works with Gmail. I tried but didn't find a way to change it, but perhaps there might be a way I'm not aware of.

I can't vouch for this, but I believe Gmail's implementation of POP is a bit specific, and this might be a side-effect, Gmail doesn't recognize folders in traditional way, it simply shows all new messages to POP client no matter whether they appear in the Inbox or Sent folder on the outside.